Finite Group Databasebeta

← Group #10698213

Character table — Group #10698213

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424248888888844121212124444444422
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-2000000000000000000000000000000002200-2-200
χ10222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-200000000000000000000000000000000-2-2002200
χ11222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-20000000000000000000000000000002200-2-20000
χ12222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-2000000000000000000000000000000-2-200220000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000002-222-2-20000000000
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000-22-2-2220000000000
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-13333−3−3−3−33333−3−3−3−3000000002-2-1-1110000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-13333−3−3−3−3−3−3−3−3333300000000-2211-1-10000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-1−3−3−3−333333333−3−3−3−300000000-2211-1-10000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-1−3−3−3−33333−3−3−3−33333000000002-2-1-1110000000000
χ232222-2-2-2-2222-222-2-2-2-2-2-2222-22-222-222-2-2-2000000002-2000000000000000000000000000000000000002-2
χ242222-2-2-2-2222-222-2-2-2-2-2-2222-22-222-222-2-2-2000000002-200000000000000000000000000000000000000-22
χ252222-2-2-2-2222-2-2-22-22-2-2-2222-2-2222-2-2-22-222i2i−2i−2i0000-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ262222-2-2-2-2222-2-2-22-22-2-2-2222-2-2222-2-2-22-22−2i−2i2i2i0000-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ272222-2-2-2-22-2-2222-22-2-2-2-2222-2-22-2-2222-22-200002i2i−2i−2i-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ282222-2-2-2-22-2-2222-22-2-2-2-2222-2-22-2-2222-22-20000−2i−2i2i2i-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ292222-2-2-2-22-2-22-2-2222-2-2-2222-22-2-2-22-2-2222000000002-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000000000
χ302222-2-2-2-22-2-22-2-2222-2-2-2222-22-2-2-22-2-2222000000002-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000000000
χ312222-2-2-2-2-122-2-2-22-22111-1-1-11-22-1-1111-11-12i2i−2i−2i00001-1−i−iii−i−iii−i3−i3i3i3i3i3−i3−i300000000003−33−30000000000
χ322222-2-2-2-2-122-2-2-22-22111-1-1-11-22-1-1111-11-12i2i−2i−2i00001-1−i−iii−i−iiii3i3−i3−i3−i3−i3i3i30000000000−33−330000000000
χ332222-2-2-2-2-122-2-2-22-22111-1-1-11-22-1-1111-11-1−2i−2i2i2i00001-1ii−i−iii−i−i−i3−i3i3i3i3i3−i3−i30000000000−33−330000000000
χ342222-2-2-2-2-122-2-2-22-22111-1-1-11-22-1-1111-11-1−2i−2i2i2i00001-1ii−i−iii−i−ii3i3−i3−i3−i3−i3i3i300000000003−33−30000000000
χ352222-2-2-2-2-1-2-2222-22-2111-1-1-11-2211-1-1-11-1100002i2i−2i−2i1-1−i3−i3i3i3i3i3−i3−i3−i−iii−i−iii0000000000−333−30000000000
χ362222-2-2-2-2-1-2-2222-22-2111-1-1-11-2211-1-1-11-1100002i2i−2i−2i1-1i3i3−i3−i3−i3−i3i3i3−i−iii−i−iii00000000003−3−330000000000
χ372222-2-2-2-2-1-2-2222-22-2111-1-1-11-2211-1-1-11-110000−2i−2i2i2i1-1−i3−i3i3i3i3i3−i3−i3ii−i−iii−i−i00000000003−3−330000000000
χ382222-2-2-2-2-1-2-2222-22-2111-1-1-11-2211-1-1-11-110000−2i−2i2i2i1-1i3i3−i3−i3−i3−i3i3i3ii−i−iii−i−i0000000000−333−30000000000
χ3922-2-222-2-220002-220-22-2-22-2-22000002-220-2−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i20000000022−2−222−2−200000000002i−2i0000
χ4022-2-222-2-220002-220-22-2-22-2-22000002-220-2−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i200000000−2−222−2−2220000000000−2i2i0000
χ4122-2-222-2-220002-220-22-2-22-2-22000002-220-2i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i20000000022−2−222−2−20000000000−2i2i0000
χ4222-2-222-2-220002-220-22-2-22-2-22000002-220-2i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i200000000−2−222−2−22200000000002i−2i0000
χ4322-2-2-2-2222000-2220-2-2222-2-2-200000-2220-22−2−220000002−2−222−2−2200000000−i2−i2i2i2i2i2−i2−i20000002i−2i00000000
χ4422-2-2-2-2222000-2220-2-2222-2-2-200000-2220-22−2−220000002−2−222−2−2200000000i2i2−i2−i2−i2−i2i2i2000000−2i2i00000000
χ4522-2-2-2-2222000-2220-2-2222-2-2-200000-2220-2−222−2000000−222−2−222−200000000−i2−i2i2i2i2i2−i2−i2000000−2i2i00000000
χ4622-2-2-2-2222000-2220-2-2222-2-2-200000-2220-2−222−2000000−222−2−222−200000000i2i2−i2−i2−i2−i2i2i20000002i−2i00000000
χ472-22-22-22-222-22000-20-22-2-22-22002-22000-200000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000002i−2i00
χ482-22-22-22-222-22000-20-22-2-22-22002-22000-200000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000−2i2i00
χ492-22-22-22-222-22000-20-22-2-22-22002-22000-200000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000−2i2i00
χ502-22-22-22-222-22000-20-22-2-22-22002-22000-200000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000002i−2i00
χ512-22-2-22-222-222000-202-22-22-2-200-222000-2000002−2−2200000000002−2−222−2−22−i2i2−i2i2i2−i2i2−i2000000002i−2i000000
χ522-22-2-22-222-222000-202-22-22-2-200-222000-2000002−2−2200000000002−2−222−2−22i2−i2i2−i2−i2i2−i2i200000000−2i2i000000
χ532-22-2-22-222-222000-202-22-22-2-200-222000-200000−222−20000000000−222−2−222−2−i2i2−i2i2i2−i2i2−i200000000−2i2i000000
χ542-22-2-22-222-222000-202-22-22-2-200-222000-200000−222−20000000000−222−2−222−2i2−i2i2−i2−i2i2−i2i2000000002i−2i000000
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-4-2-2-2222-2200000000220000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4222-2-2-22-200000000220000000000000000000000000000000000000000
χ574444-4-4-4-4-244-444-4-4-4222-2-2-224-4-2-22-2-222200000000-220000000000000000000000000000000000000000
χ584444-4-4-4-4-2-4-44-4-4444222-2-2-224-422-222-2-2-200000000-220000000000000000000000000000000000000000
χ5944-4-444-4-44000-44-4044-4-44-4-4400000-44-40400000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-20004-440-4-222-222-200000-22-202−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ6144-4-444-4-4-20004-440-4-222-222-200000-22-2022i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ6244-4-444-4-4-2000-44-404-222-222-2000002-220-20000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ6344-4-444-4-4-2000-44-404-222-222-2000002-220-20000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ6444-4-4-4-44440004-4-404-4444-4-4-4000004-4-40400000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-20004-4-4042-2-2-222200000-2220-200000000006−6−66−666−600000000000000000000000000000000
χ6644-4-4-4-444-20004-4-4042-2-2-222200000-2220-20000000000−666−66−6−6600000000000000000000000000000000
χ6744-4-4-4-444-2000-4440-42-2-2-2222000002-2-20222−22−2222000000−222−2−222−200000000000000000000000000000000
χ6844-4-4-4-444-2000-4440-42-2-2-2222000002-2-202−222222−220000002−2−222−2−2200000000000000000000000000000000
χ694-44-44-44-44-44-400040-44-4-44-4400-44-40004000000000000000000000000000000000000000000000000000
χ704-44-44-44-4-24-44000-402-222-22-200-22-2000200000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ714-44-44-44-4-24-44000-402-222-22-200-22-20002000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ724-44-44-44-4-2-44-4000402-222-22-2002-22000-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ734-44-44-44-4-2-44-4000402-222-22-2002-22000-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ744-44-4-44-4444-4-4000404-44-44-4-4004-4-40004000000000000000000000000000000000000000000000000000
χ754-44-4-44-44-24-4-400040-22-22-22200-222000-200000000000000000006−6−66−666−6000000000000000000000000
χ764-44-4-44-44-24-4-400040-22-22-22200-222000-20000000000000000000−666−66−6−66000000000000000000000000
χ774-44-4-44-44-2-444000-40-22-22-222002-2-200020000022−22−22220000000000−222−2−222−2000000000000000000000000
χ784-44-4-44-44-2-444000-40-22-22-222002-2-2000200000−222222−2200000000002−2−222−2−22000000000000000000000000
χ794-4-444-4-44400000000-4-44-4-4440000000000000000000000000000000000002-2-222-2-220000000000000000
χ804-4-444-4-44400000000-4-44-4-444000000000000000000000000000000000000-222-2-222-20000000000000000
χ814-4-44-444-440000000044-4-4-44-40000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ824-4-44-444-440000000044-4-4-44-4000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ838-8-888-8-88-40000000044-444-4-4000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).